Given the following integral SV2-25 ox Determine the Trigonometric Substitution formulas that need to be used for this integral.

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Question 004: Complete the following question involving Trigonometric Substitution
Given the following integral
SV2 - 25 ox
Determine the Trigonometric Substitution formulas that need to be used for this integral.
A
Ssec(e)
dx
5sec(e)tan(e) de
x2. 25
25tan?(e)
A
5sin(e)
dx
Scos(e) de
x2- 25
25cos (e)
A
5tan(e)
dx
5sec(e)tan(e) de
x2- 25
25tan2(e)
A
25
25tan(e)
25sec2(e) de
dx
x2- 25
25sec?(e)
Transcribed Image Text:Question 004: Complete the following question involving Trigonometric Substitution Given the following integral SV2 - 25 ox Determine the Trigonometric Substitution formulas that need to be used for this integral. A Ssec(e) dx 5sec(e)tan(e) de x2. 25 25tan?(e) A 5sin(e) dx Scos(e) de x2- 25 25cos (e) A 5tan(e) dx 5sec(e)tan(e) de x2- 25 25tan2(e) A 25 25tan(e) 25sec2(e) de dx x2- 25 25sec?(e)
Expert Solution
Step 1

The given integral is:

I=x2-25dx

Trigonometric relation used is:

tan2x+sec2y=1

The given integral is easy to solve by trigonometric substitution:

 

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